标题： 朝向格点QCD中$T_{cc}^+$的夸克质量依赖性 显示英文标题

标题： Towards the quark mass dependence of $T_{cc}^+$ from lattice QCD

摘要： 在$DD^*$通道中，$T_{cc}^+=cc\bar{u}\bar{d}$的散射相移从格点 QCD 中提取出来，针对五种不同的重夸克质量以及对应于$m_\pi\simeq 280$~MeV 的固定轻夸克质量。 相移通过两种方法进行分析：有效范围展开和由有效场论导出的 Lippmann--Schwinger 方程。 在后一种情况下，结果表明短程存在由接触项参数化的吸引力，以及由一介子交换引起的长程轻微排斥，其值为$m_\pi >m_{D^*}-m_D$。 在复能量平面上，振幅中的极点被提取出来，并随着重夸克质量的变化讨论了它们的轨迹。 对于$m_c$接近物理值的情况，发现两个对应于阈值以下共振的共轭复数极点。 当研究最大的$m_c$时，它们转变为一对虚态。 随着$m_c$的进一步增加，一个代表$T_{cc}^+$的虚拟极点预计将向两个体阈值移动并转变为束缚态。 $T_{cc}^+$极点的轻夸克质量依赖性通过其他格点合作组关于$DD^*$散射的数据进行了简要讨论。 显示英文摘要

摘要： The $DD^*$ scattering phase shifts in the $T_{cc}^+=cc\bar{u}\bar{d}$ channel are extracted from lattice QCD for five different charm quark masses and a fixed light-quark mass corresponding to $m_\pi\simeq 280$~MeV. The phase shifts are analysed employing two approaches: effective range expansion and Lippmann--Schwinger equation derived in the effective field theory. In the latter case, the results imply an attraction at short range parametrised by contact terms and a slight repulsion at long range mediated by one-pion exchange with $m_\pi >m_{D^*}-m_D$. The poles in the amplitude across the complex energy plane are extracted and their trajectories are discussed as the charm quark mass is varied. Two complex conjugate poles corresponding to a resonance below threshold are found for $m_c$ close to the physical value. They turn into a pair of virtual states at the largest $m_c$ studied. With further increasing $m_c$, one virtual pole representing $T_{cc}^+$ is expected to move towards the two-body threshold and turn into a bound state. The light-quark mass dependence of the $T_{cc}^+$ pole is briefly discussed using the data on $DD^*$ scattering from other lattice collaborations.